Your specific question is about why uniform gas is a low entropy state for the universe. The reason is that you make entropy by allowing the gas to self-gravitate and compress, releasing heat to the environment in the process. The end result is a black hole where the gas is compressed maximally, and these are the maximum entropy gravitational states.
But the uniform gas comes from a nearly uniform inflaton field shaking over all space after inflation. This inflaton produces uniform denisty of matter, which then becomes uniform baryons and hydrogen. Ultimately, it is the uniformity of the energy density in the inflaton field which is responsible for the low entropy of the initial conditions, and this is linked to the dynamics of inflation.
The dynamics of inflation produce low entropy initial conditions without fine tuning. This seems like a paradox, because low entropy is fine tuning by definition, don't you need to choose a special state to have low entropy? The answer in inflation is that the state is only special in that there is a large positive cosmological constant, but it is otherwise generic, in that it is a maximum entropy state given the large cosmological constant.
The theory of inflation explains the specialness of the initial conditions completely. This was proposed by Davies in 1983, but it is rejected by cosmologists. The rest of this answer discusses arguments that support Davies' position.
deSitter space
If you consider a deSitter space with some mass density added, and you look in a causal patch (meaning what one observer can see), the mass density gives an additional curvature without (significant) pressure and turns deSitter into more like a sphere. There is a continuous deformation of deSitter space into the Einstein static universe, which is obtained by making the density of matter as large as possible.
Any matter you add reduces the horizon area of the cosmological horizon, and this is true for black holes as well. If you consider the ds-Schwartschild exact solution, for example, you can have an isolated black hole in deSitter space:
$$ \rm ds^2 = - f(r) \rm dt^2 + {\rm dr^2\over f(r) } + r^2 \rm d\Omega^2 $$
$$ f(r) = 1 - {2m\over r} - {\Lambda r^2\over 3} $$
but there are two horizons, and the causal patch is the region between the black hole and the cosmological horizon. It is easy to check that the total horizon area, cosmological plus black-hole is maximum for m=0. It is also easy to check that there is a certain value of m where the black hole radius and the cosmological radius degenerate. At this degeneration, the distance between the black hole and cosmological horizon stays constant, they do not collide except in the bad r coordinate, and the space turns into AdS_2 x S_2.
Nariai dynamics
Imagine starting near a Nariai solution with additional matter between the two horizons. These are both still black holes, neither is a cosmological horizon, as you can see by adding more matter with a uniform density, until you approach the limit of the Einstein static universe with two antipodal black holes.
This is a physical configuration of the static cosmology. So you can start with an Einstein static universe, and evolve it forward in time, you will produce black holes, and they will merge and grow.
If you take all the matter in the static universe and push it into one of the black holes, this black hole area will increase past the Nariai limit and it will become the cosmological horizon. At this point, the singularity runs away to infinity. If you push the matter into another black hole, the other black hole will be the cosmological horizon. It's up to you.
So if you start with the Einstein static universe, the black holes compete for mattter, until eventually the biggest black hole will surround all the others, and become the cosmological horizon.
The lessons are the following:
- Cosmological horizons are the same stuff as black hole horizons. Their other side is described by black hole complementarity, just as for black holes. It is wrong to think of the universe in a global picture.
- deSitter space is the maximum entropy configuration of a positive cosmological constant universe, everything else eventually thermalizes into deSitter space.
- The global picture of black holes is not particularly physical, because the singularity of the Nariai solution runs away to infinity in the Nariai limit. There are cases where black hole interior structure degenerates.
Inflation Produces Low Entropy Initial Conditions
The second point answers your question, because the early universe is in a deSitter phase. So given a large positive value of the cosmological constant in the early universe, the maximum entropy state is a deSitter space with a cosmological horizon of small area, and this is necessarily a low entropy initial condition for later times, during which the cosmological horizon grows.
There is no further explanation required for the low-entropy initial conditions. This is the same explanation as for all the other miracles of inflation, the killing of fluctuations, the flatness condition, the monopole problem. The whole point of inflation is to produce a theory of low entropy initial conditions, including gravity, and it does so naturally, because deSitter space is the only low entropy maximal entropy gravitational state. This answer was first given by Davies, and it is just plain correct.
This plain-as-the-nose-on-your-face idea is not accepted despite the nearly thirty years since Davies' paper. I should add that Tom Banks and Leonard Susskind both now say similar things, although I don't want to put words in their mouths.
The CMB origin at about 380,000 years after the Big Bang is indeed the furthest we can see, IN THE ELECTROMAGNETIC spectral domain. And you are right that this is not about the full universe vs the observable universe, you are talking about a portion of the observable universe which is simply occluded from us not in principle, but because photons could not propagate from freely out until then.
So, theoretically the universe is about 13.8 billion years old, and we can 'see' into the past only to 380,000 years after the Big Bang.
The reason we don't stop there, in either theory or in understanding what's behind that apparent 'wall', is that 1) we know a lot about what happened before the 380,000 year 'wall' from what needed to be there in order for us to see what we see after, AND maybe more important
2) for those who don't believe what they can't see, we will be able to see behind the 'wall' with gravitational waves.
Gravitational waves (GWs) are affected little by that 'wall' and all we need to do is build a large enough interferometer pair, to see them. LIGO which detected GWs from black holes merging, cannot detect those cosmologically originated GWs because their wavelengths are much larger. We need space based interferometers with legs a million Kms or larger -- that's in the planning for the next decade, with 2 or 3 satellites forming the 1 or 3 legs (funding dependent). And later bigger ones. We spect to see behind the wall using that gravitational astronomy.
As for your 3 questions:
Matter behinds the wall. We know there had to be matter, but it was mostly uncondensed and very energetic charged particles, mostly electrons and protons. At 380,000 years they recombined into hydrogen atoms and a few other things, and the photons we see now as the CMB could escape. We know actually a lot more, eg, about the very small inhomogeneities and anisotropies in the CMB which came from the same on the density of matter, and which served as seeds of galaxies and stars. Before electrons and protons it was even hotter, and it was quarks, gluons and electrons and a few other particles, and before that particles we have not seen in the lab. We know the basic physics for those things but still expect there will be more energetic particles, perhaps remnants of the Big Bang that became dark matter, and other exotic particles. As it gets hotter it's quantum gravity like string theory claims, and for which we still don't know what the right theory is.
We do think we know that there are galaxies that we can not see now. Even many of the ones we see now, emitted their light long ago, and will not see their light emittEd now ever. They are traveling away from us now too fast, and light emitted from them will never reach us. But we are seeing the light from many such galaxies now, that they emitted billions of years ago. Yes, the cosmological horizon is, we think, real
Nothing overtook the CMB. Galaxies and stars were formed maybe a few million years after tHe CMB broke free. Remember the universe was expanding, so if they are younger than the CMB they were created closer to us, and it's why we can see them. General Relativistic geometry can be tricky, but for cosmology it's good to think in terms of time from the Big Bang or back from us. Keep in mind the CMB was released everywhere in space, and what we see now are photons that reached us now. They traveled for 13.8 billion minus 380,000 years. We have seen galaxies going back to a couple hundred million years from the Big Bang (but sorry, I may not have the number exactly right, or most updated).
For an intro to the chronology of the universe see the wiki article at
https://en.m.wikipedia.org/wiki/Chronology_of_the_universe
It's got the different cosmological periods or epochs, including the recombination time (the 'wall') and other important cosmological times. We still have a lot to learn, but the most mysterious epochs from our knowledge of elementary particle physics are those that are the earliest: the Planck epoch (we just don't know what makes thing up then, maybe string theory or other quantum gravity theory will get to it sometime), the strong unification era (we know a little bit after how and when the stron and electroweak force unify, but still plenty uncertainty), and the inflationary epoch (we have inflation theories, some version seems right but we're not sure which, or the field that caused it). We tend to know a lot about the rest, from theory and observation, but still we think we'll find surprises.
Your final two questions:
A. The current observable universe is about 46 billion light years in radius. We see pretty far out, but have not seen the edge, or what is called the horizon (we would not fall off). Unfortunately, if anybody is around in a quite few billions of years we will see even the closest galaxies get too far from us to be able to see them (or their successors) because the expansion will have taken them past our then horizon
B. There will always be CMB around as they were created everywhere in space. However, they will be way way redshifted- right now they've been redshifted by a factor of 1100, and we see it as high microwaves, 100 Ghz range. Another factor of a million say they'll be 100 KHz but much weaker, and eventually they'll get too weak and low frequency for us to detect.
Best Answer
You heard wrong. There were photons, electrons, protons, and neutrons before 300,000 years. And before 3 minutes! (And before there were protons and neutrons, there were quarks.)
Before 300,000 years, the photons could not propagate freely; they were being constantly scattered by the charged plasma of protons and electrons. The universe was effectively opaque.
Around 300,000 years, the universe had cooled enough that protons and electrons could form hydrogen atoms. A few other light elements also formed, because protons and neutrons had earlier formed helium nuclei, etc.
Atoms are overall electrically neutral and do not scatter photons nearly as much as a charged plasma does. So, after 300,000 years, the photons could move right through the neutral hydrogen gas. The universe became transparent. Cosmic photons created in the Big Bang have been moving without scattering for billions of years since “recombination”, the formation of neutral atoms.